Bodenstein, S., Bordes, J., Dominguez, C. A., Peñarrocha, J., & Schilcher, K. (2010). Charm-quark mass from weighted finite energy QCD sum rules. Phys. Rev. D, 82(11), 114013–5pp.
Abstract: The running charm-quark mass in the scheme is determined from weighted finite energy QCD sum rules involving the vector current correlator. Only the short distance expansion of this correlator is used, together with integration kernels (weights) involving positive powers of s, the squared energy. The optimal kernels are found to be a simple pinched kernel and polynomials of the Legendre type. The former kernel reduces potential duality violations near the real axis in the complex s plane, and the latter allows us to extend the analysis to energy regions beyond the end point of the data. These kernels, together with the high energy expansion of the correlator, weigh the experimental and theoretical information differently from e. g. inverse moments finite energy sum rules. Current, state of the art results for the vector correlator up to four-loop order in perturbative QCD are used in the finite energy sum rules, together with the latest experimental data. The integration in the complex s plane is performed using three different methods: fixed order perturbation theory, contour improved perturbation theory, and a fixed renormalization scale mu. The final result is (m) over bar (c)(3 GeV) = 1008 +/- 26 MeV, in a wide region of stability against changes in the integration radius s(0) in the complex s plane.
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Bodenstein, S., Bordes, J., Dominguez, C. A., Peñarrocha, J., & Schilcher, K. (2011). QCD sum rule determination of the charm-quark mass. Phys. Rev. D, 83(7), 074014–4pp.
Abstract: QCD sum rules involving mixed inverse moment integration kernels are used in order to determine the running charm-quark mass in the (MS) over bar scheme. Both the high and the low energy expansion of the vector current correlator are involved in this determination. The optimal integration kernel turns out to be of the form p(s) = 1 -(s(0)/s)(2), where s(0) is the onset of perturbative QCD. This kernel enhances the contribution of the well known narrow resonances, and reduces the impact of the data in the range s similar or equal to 20-25 GeV2. This feature leads to a substantial reduction in the sensitivity of the results to changes in s(0), as well as to a much reduced impact of the experimental uncertainties in the higher resonance region. The value obtained for the charm-quark mass in the (MS) over bar scheme at a scale of 3 GeV is (m) over bar (c)(3 GeV) = 987 +/- 9 MeV, where the error includes all sources of uncertainties added in quadrature.
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Bodenstein, S., Bordes, J., Dominguez, C. A., Peñarrocha, J., & Schilcher, K. (2012). Bottom-quark mass from finite energy QCD sum rules. Phys. Rev. D, 85(3), 034003–5pp.
Abstract: Finite energy QCD sum rules involving both inverse-and positive-moment integration kernels are employed to determine the bottom-quark mass. The result obtained in the (MS) over bar scheme at a reference scale of 10 GeV is m (m) over bar (b)(10 GeV) = 3623(9) MeV. This value translates into a scale-invariant mass (m) over bar (b)((m) over bar (b)) = 4171(9) MeV. This result has the lowest total uncertainty of any method, and is less sensitive to a number of systematic uncertainties that affect other QCD sum rule determinations.
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Baker, M. J., Bordes, J., Hong-Mo, C., & Tsun, T. S. (2013). On the corner elements of the CKM and PMNS matrices. EPL, 102(4), 41001–6pp.
Abstract: Recent experiments show that the top-right corner element (U-e3) of the PMNS matrix is small but nonzero, and suggest further via unitarity that it is smaller than the bottom-left corner element (U-tau 1). Here, it is shown that if to the assumption of a universal rank-one mass matrix, long favoured by phenomenologists, one adds that this matrix rotates with scale, then it follows that A) by inputting the mass ratios m(c)/m(t), m(s)/m(b), m(mu)/m(tau), and m(2)/m(3), i) the corner elements are small but nonzero, ii) V-ub < V-td, U-e3 < U-tau 1, iii) estimates result for the ratios V-ub/V-td and U-e3/U-tau 1, and B) by inputting further the experimental values of V-us, V-tb and U-e2, U-mu 3, iv) estimates result for the values of the corner elements themselves. All the inequalities and estimates obtained are consistent with present data within expectation for the approximations made.
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Bordes, J., Chan, H. M., & Tsun, T. S. (2010). Possible anomalies in Higgs decay: charm-suppression and flavour-violation. Eur. Phys. J. C, 65(3-4), 537–542.
Abstract: It is suggested that the Higgs boson may have a branching ratio into the c (c) over bar c mode suppressed by several orders of magnitude compared with conventional predictions and in addition some small but detectable flavour-violating modes such as b (s) over bar and tau(mu) over bar. The suggestion is based on a scheme proposed and tested earlier for explaining the mixing pattern and mass hierarchy of fermions in terms of a rotating mass matrix. If confirmed, the effects would cast new light on the geometric origin of fermion generations and of the Higgs field itself.
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